27 citations · 78 across the 9 of their papers we have counts for
10 papers
Fully nonlinear gravitational instabilities for expanding spherical symmetric Newtonian universes with inhomogeneous density and pressure
Chao Liu
Nobel Prize laureate P.J.E. Peebles [24] has emphasized the importance and difficulties of studying the large scale clustering of matter in cosmology. Nonlinear gravitational insta…
Ricci Flow method in the existence problem of the K"ahler-Einstein metrics
Liu Chao
This note illustrates the Ricci flow method based on the Cao.H.D's paper[1] and Yau.S.T's paper[4], and tries to explain the method in detail, especially in some calculations. Jian…
Fully nonlinear gravitational instabilities for expanding Newtonian universes with inhomogeneous pressure and entropy: Beyond the Tolman's solution
Chao Liu
Nonlinear gravitational instability is a crucial way to comprehend the clustering of matter and the formation of nonlinear structures in both the Universe and stellar systems. Howe…
Blowups for a class of second order nonlinear hyperbolic equations: A reduced model of nonlinear Jeans instability
Chao Liu
Understanding the formation of nonlinear structures in the universe and stellar systems is crucial. The nonlinear Jeans instability plays a key role in these formation processes. I…
Rigorous proof of slightly nonlinear Jeans instability in the expanding Newtonian universe
Chao Liu, Yiqing Shi
Due to the nonlinearity of the Euler{Poisson equations, it is possible that the nonlinear Jeans instability may lead to a faster density growing rate than the rate in the standard…
Future global existence and stability of de Sitter-like solutions to the Einstein-Yang-Mills equations in spacetime dimensions
Chao Liu, Todd A. Oliynyk, Jinhua Wang
We establish the global existence and stability to the future of non-linear perturbation of de Sitter-like solutions to the Einstein-Yang-Mills system in spacetime dimen…
A new symmetric hyperbolic formulation and the local Cauchy problem for the Einstein--Yang--Mills system in the temporal gauge
Chao Liu, Jinhua Wang
Motivated by the future stability problem of solutions of the Einstein--Yang--Mills (EYM) system with arbitrary dimension, we aim to (1) construct a tensorial symmetric hyperbolic…
Future stability of the FLRW spacetime for a large class of perfect fluids
Chao Liu, Changhua Wei
We establish the future non-linear stability of Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) solutions to the Einstein-Euler equations of the universe filled with a large class of…
Cosmological Newtonian limits on large spacetime scales
Chao Liu, Todd A. Oliynyk
We establish the existence of -parameter families of -dependent solutions to the Einstein-Euler equations with a positive cosmological constant and a linear equation of…
Newtonian Limits of Isolated Cosmological Systems on Long Time Scales
Chao Liu, Todd A. Oliynyk
We establish the existence of -parameter families of -dependent solutions to the Einstein-Euler equations with a positive cosmological constant and a linear equation of…